Spontaneous CP violation in the Supersymmetric Higgs Sector

Spontaneous CP--violation in the minimal supersymmetric standard model with a gauge singlet and a cubic superpotential is examined. Although the tree--level Higgs potential conserves CP, it is shown that with the inclusion of the one--loop top--quark radiative effects, CP may be broken spontaneously. The CP--violating minimum requires two neutral $(h_1,h_2)$ and one charged $(H^\pm)$ Higgs--bosons to be relatively light with $m_{h_1}+m_{h_2} \stackrel{_<}{_\sim} 100~GeV$ and $m_{H^\pm} \stackrel{_<}{_\sim} 110~GeV$. The electric dipole moment of the electron is in the observable range of $({1 \over 3}~{\rm to}~3) \times 10^{-27}$e-cm.